How many numbers between $1$ and $100$ (inclusive) are divisible by $10$ or $7$ ?
There are $10$ numbers divisible by $10$ between $1$ and $100$, and $14$ numbers divisible by $7$ between $1$ and $100$. So, you might think there are $10 + 14 = 24$ numbers divisible by one or the other, but this is overcounting something. We're counting every number which is divisible by both $10$ and $7$ twice. So, for example, $70$ is counted once as a number divisible by $10$, and then again as a number divisible by $7$. So, we need to count how many numbers are divisible by both $10$ and $7$ and subtract this from what we had before. Being divisible by both $10$ and $7$ is the same thing as being divisible by $70$, so there is $1$ number between $1$ and $100$ divisible by both. Subtracting, there are $24 - 1 = 23$ numbers divisible by $10$ or $7$.